In this work, the spinodal phase demixing of branched comb polymer
nanocomposite (PNC) melts is systematically investigated using the
polymer reference interaction site model (PRISM) theory. To verify the
reliability of the present method in characterizing the phase behavior
of comb PNCs, the intermolecular correlation functions of the system for
nonzero particle volume fractions are compared with our molecular
dynamics simulation data. After verifying the model and discussing the
structure of the comb PNCs in the dilute nanoparticle limit, the
interference among the side chain number, side chain length,
nanoparticle-monomer size ratio and attractive interactions between the
comb polymer and nanoparticles in spinodal demixing curves is analyzed
and discussed in detail. The results predict two kinds of distinct phase
separation behaviors. One is called classic fluid phase boundary, which
is mediated by the entropic depletion attraction and contact aggregation
of nanoparticles at relatively low nanoparticle-monomer attraction
strength. The second demixing transition occurs at relatively high
attraction strength and involves the formation of an equilibrium
physical network phase with local bridging of nanoparticles. The phase
boundaries are found to be sensitive to the side chain number, side
chain length, nanoparticle-monomer size ratio and attractive
interactions. As the side chain length is fixed, the side chain number
has a large effect on the phase behavior of comb PNCs; with increasing
side chain number, the miscibility window first widens and then shrinks.
When the side chain number is lower than a threshold value, the phase
boundaries undergo a process from enlarging the miscibility window to
narrowing as side chain length increases. Once the side chain number
overtakes this threshold value, the phase boundary shifts towards less
miscibility. With increasing nanoparticle-monomer size ratio, a
crossover of particle size occurs, above which the phase separation is
consistent with that of chain PNCs. The miscibility window for this
condition gradually narrows while the other parameters of the PNCs
system are held constant. These results indicate that the present PRISM
theory can give molecular-level details of the underlying mechanisms of
the comb PNCs. It is hoped that the results can be used to provide
useful guidance for the future design control of novel,
thermodynamically stable comb PNCs.